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SYLLABUS

UNIT-1

Differential Equations of First Order and First Degree Introduction - Equations in Which Variables are Separable - Homogeneous Differential Equations - Differential Equations Reducible to Homogeneous Form - Linear Differential Equations - Differential Equations Reducible to Linear Form - Exact Differential Equations - Integrating Factors - Change in Variables - Total Differential Equations - Simultaneous Total Differential Equations - Equations of the Form P dx Q dy R dz = =

UNIT-2

Differential Equations of First Order But Not of First Degree Equations Solvable for p - Equations Solvable for y - Equations Solvable for x - Equations that do not contain x (or y)- Equations Homogeneous in x and y - Equations of the First Degree in x and y - Clairaut’s Equation. Applications of First Order Differential Equations : Growth and Decay - Dynamics of Tumour Growth - Radio Activity and Carbon Dating - Compound Interest - Orthogonal Trajectories

UNIT-3

Higher Order Linear Differential Equations Solution of Homogeneous Linear Differential Equations with Constant Coefficients - Solution of Non - Homogeneous Differential Equations P(D)y = Q(x) with Constant Coefficients by Means of Polynomial Operators When Q(x) = beax; b sin ax ! b cos ax; bxk ; V eax - Method of Undetermined coefficients.

UNIT-4

Higher Order L.D.E and Partial Differential Equations Method of Variation of Parameters - Linear Differential Equations with Non Constant Coefficients - The Cauchy-Euler Equation - Legendre’s Linear Equations - Miscellaneous Differential Equations. Partial Differential Equations : Formation and Solution - Equations easily Integrable - Linear Equations of First Order.